principal_axes_inertiaΒΆ
Transform the inertia tensor \(\boldsymbol{j}_a\) defined about the A
frame of reference to the centre of
gravity and aligned with the principal axes of inertia.
The inertia tensor about the centre of gravity is obtained using the parallel axes theorem
\[\boldsymbol{j}_{cm} = \boldsymbol{j}_a + \tilde{r}_{cg}\tilde{r}_{cg}m\]
and rotated such that it is aligned with its eigenvectors and thus represents the inertia tensor about the principal axes of inertia
\[\boldsymbol{j}_p = T_{pa}^\top \boldsymbol{j}_{cm} T^{pa}\]
where \(T^{pa}\) is the transformation matrix from the A
frame to the principal axes P
frame.
- param j_a
Inertia tensor defined about the
A
frame.- type j_a
np.array
- param r_cg
Centre of gravity position defined in
A
coordinates.- type r_cg
np.array
- param m
Mass.
- type m
float
- returns
Containing \(\boldsymbol{j}_p\) and \(T^{pa}\)
- rtype
tuple